] Have Jane Austen ever mentioned racing or betting or other types of playing for money in her novels or letters? (snip) But would the men play for money at those cardgames they sometimes had at the balls?

Well, Tom Bertram gambled so heavily that Sir Thomas had to sell the family living. And it was probably racing, as Newmarket was mentioned as the place where he had got his fateful fever. Though, I don't know, perhaps he played cards, too.

Card playing more or less lost its sinister reputation of heavy gambling, got in the 18th century, and it was a normal feature of every ball, or there could be a special card party (like one that Miss Elliot gathered at the end of Persuasion). Among mentions of card-playing at balls my favorite is in The Watsons, when Mr Edwards remarks on brilliancy of the ball, though how he could notice it, JA says a parte, without getting from the card table, beats her.

People at such gatherings invariably played for money, I gather. It needn't be big money, but still. When Mrs Norris tries to pull Tom Bertram into a game of whist, she says in so many words, though we play for half-crowns, you may stake guineas with Dr. Grant. And it was just a neighbourly evening, when young people danced, and Fanny sat without a partner. The only situation of playing without stakes, I imagine, was in the closest family, like Fanny playing cribbage with Lady B.